{"title":"An Overview of Minimum Convex Cover and Maximum Hidden Set","authors":"Reilly Browne","doi":"arxiv-2403.01354","DOIUrl":null,"url":null,"abstract":"We give a review of results on the minimum convex cover and maximum hidden\nset problems. In addition, we give some new results. First we show that it is\nNP-hard to determine whether a polygon has the same convex cover number as its\nhidden set number. We then give some important examples in which these\nquantities don't always coincide. Finally, We present some consequences of\ninsights from Browne, Kasthurirangan, Mitchell and Polishchuk [FOCS, 2023] on\nother classes of simple polygons.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.01354","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We give a review of results on the minimum convex cover and maximum hidden
set problems. In addition, we give some new results. First we show that it is
NP-hard to determine whether a polygon has the same convex cover number as its
hidden set number. We then give some important examples in which these
quantities don't always coincide. Finally, We present some consequences of
insights from Browne, Kasthurirangan, Mitchell and Polishchuk [FOCS, 2023] on
other classes of simple polygons.
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